A Scattered Repository

Primary Menu

Least Disruptive Subrange Coding Interview Problem

Here’s the code from the first episode. This is a basic coding interview question that you might be asked in an interview at a tech company. You can see the video associated with this code here:

The problem here can be stated pretty simply. Imagine that you need a function that can take two inputs: 1) a list of integers and 2) another list of integers. The first list could be thousands of integers long. It can contain positive and negative numbers. It’s not sorted in any way. Any integer could be at any position. The second list is similar except that it’s equal in length to the first list or shorter.

What we want to do with these lists is find where in the first list we could substitute the second list, integer for integer, that would create the least amount of change in each integer from the original list. For this problem, we consider change to be measured in number line distance (i.e. absolute value). So, you can’t use some negative distance to offset some positive distance. If you substitute -2 for 2, that’s a change of 4.

An example would be something like this:

original = [1, 2, 3, 4, 5]
replacement = [3, 5, 3]

In this example, the “disruption” created by each possible substitution looks like this:

You can see from this, that the best replacement choice here would be the 2nd index, which would create a subrange disruption of just 3, compared to all the other options.

So how might you solve this? Well, here’s a bit of JavaScript that aims to tackle the problem. This algorithm runs in O(n*m) time, where n refers to the length of the first input and m is the length of the second input. Interestingly, the longer the second input is, the shorter the run of the algorithm will be. So, the worst case is something like the length of replacement being half the length of original. In that case, the algorithm will do something along the lines of m*m work. It’s a constant memory problem in that it uses no additional arrays or objects to store state. I guess you could achieve this with a hash table if you just felt like wasting RAM. 😀

While this algorithm (as far as I know) is correct, it does leave many details unserved. For instance, I don’t address the potential to integer underflow by subtracting from the minimum integer value in JavaScript. Likewise, I could integer overflow by adding to distance until it bubbles over the maximum integer value in JavaScript. My test cases are also fairly limited and don’t test for cases like empty list inputs. Also, because JavaScript, I should be checking for null inputs and handling that case reasonably. I’m also not checking for the case where replacement could be longer than original. I’m sure there are like a dozen other defects here.

The point is not to create a bullet-proof library function. Rather, I was aiming to simulate a real coding interview focusing on what you’d have time to accomplish. Let me know what you think. Especially let me know if I got it all wrong!

So, you’re totally right that I got it wrong at first. I had O(n*m) originally but then someone convinced me I was wrong so I changed it. I’ve now changed it back to O(n*m), which is correct. So, I’m afraid that you’re not right about the O(n^2) here. As far as I can tell, the algorithm for this question is identical in complexity and structure to the naive string search algorithm — https://en.wikipedia.org/wiki/String_searching_algorithm#Na.C3.AFve_string_search.